/sci/ - Science & Math

integration by parts

u = 1 + e^x
dv = 1/e^x dx

haven't worked it out but it seems like that might work

integration by parts or just expand the numerator, divide each term by the denominator.

>>3704638

expanding the numerator is probably the fastest/easiest

could someone maybe write out the first step or two?

>>3704643
seriously just expand out the numerator

>>3704643
UHHH DURRR
<span class="math">{e^2x +2 e^x + 1} \over {e^x}[/spoiler]

i figured that much out but im not seeing how it helps me

>>3704651

now divide each term by the denominator, and since you can split the integrals up for each addition, you will have 3 simple integrals to compute

>>3704643

I can't latex but okay

integral of (just assume im carrying the integral sign)
(1 + e^x)^2 / e^x
(1 + 2e^x + e^2x) / e^x
(e^-x) + 2 + e^x
= -e^-x + 2x + e^x + c

>>3704649
<div class="math"> \int {{e^{2x} +2 e^x + 1} \over {e^x} dx}</div>

>>3704651

oh ok. thank you! having a mad brain fart, its been a while since i had to do this